One hundred and six morphinan derivatives were taken from the Drug Evaluation Committee reports to propose several quantitative structure-activity relationship models to describe the mu-receptor-binding affinity. After several procedures to reduce the descriptor number, 21 descriptors were selected for the descriptor pool by a complete Multiple Linear Regression methodology. In this procedure only three molecules were considered as outliers. Several tests changing the relation between training:predicted sets were considered to find the best relation between these sets. The higher the number of molecules in the predicted set the higher the predictive power was observed. The optimal number of descriptors was established using the Akaike's information criterion and Kubinyi fitness function parameters. The Artificial Neuron Network methodology was applied to improve the Multiple Linear Regression best result. Finally, the regression through the origin methodology was applied to establish the best model from the Artificial Neuron Network methodology. The best quantitative structure-activity relationship model was proven to be independent of chance correlation.